It is often desired to isolate and determine the concentration of a particular element or species contained in an unknown sample. This is conventionally done for molecular species by a spectrometer operating, for example, in the infrared region of the spectrum. More recently, it might be accomplished for elements by an atomic emission spectrometer such as an inductively coupled plasma (ICP) spectrometer. One of the major problems in handling spectral data of this type arises from overlapped responses from various chemical species in the unknown mixture. Such responses may, for example, completely hide the response from the element or species which it is desired to measure.
One prior art technique for solving this problem is to separately measure and record the spectral responses of components known or suspected to be in the unknown sample. Coefficients are then selected which are employed to multiply each of the preselected spectral patterns such that, when summed together, they will minimize the root mean square difference between such sum and the spectral data from the sample. For example, in an abstract "A Multiple Regression Procedure for Elemental Analysis at Low Concentrations" by Z. Mencik, P.L. Berneburg and M.A. Short, Advances in X-ray Analysis 18, 396-405 (1974), multiple regression is disclosed for relating x-ray intensities to calibration standards, whereby regression coefficients are used to solve for the contents of elements in unknown samples.
Another prior art method is by use of the Kalman filter, as disclosed in an article "Some Spectral Interference Studies Using Kalman filtering in Inductively Coupled Plasma-Atomic Emission Spectroscopy" by E.H. van Veen, F.J. Oukes and M.T.C. de Loos-Vollebregt, Spectrochimica Acta 45B, 1109-1120 (1990). This is an iterative process. A set of coefficients is estimated. These coefficients are employed to multiply each data point in the spectrum. The error between the results and each data point is computed. A derivative is then estimated that indicates the direction in which to shift the estimates of the coefficients. Accordingly, there is a successive refinement of the error which, after many iterations, converges.
One of the problems with both of the aforementioned methods is that they are computational and time intensive. This becomes a particular problem in the case of ICP atomic emission spectra wherein there might be, for example, data points at 64 discrete frequencies and several unknowns. This would result in the need to solve simultaneously 64 different equations having, for example, 3 unknowns.
Another problem with the prior art techniques arises from spectral wavelength shifts in the unknown sample. Such shifts cause the peaks of components in the unknown sample to appear to be at different wavelengths than the previously recorded peaks of the pure components. Such apparent shifts may occur, for example, between instruments and even, with time, in the same instrument. In dealing with this problem, the prior art approach has been to use interpolation. The spectral information is collected at discrete points. If a wavelength shift is required, it is necessary to know what the data is between such points. However, since the amount of interpolation is not known, it is required to successively check the error and iterate. This also is a mathematically and time intensive procedure.
U.S. Pat. No. 5,023,804 (Hoult) discloses comparing spectral data with a standard spectrum by computing a normalized dot product of a sample spectrum and the standard spectrum. The two spectra are weighted by filtering to remove short and long periodicities, the filtering being effected with a triangular wave using a simplified algorithm.
U.S. Pat. No. 4,997,280 (Norris) discloses a spectrophotometric instrument in which rapid scanning causes distortion of the spectrum. A first derivative is determined from the spectrum and multiplied by a constant selected to correct for the distortion. The resulting product values are added to the distorted spectrum to provide a set of corrected values for intensity. The selected constant is determined by comparing data acquired from operation of the instrument at a normally rapid speed and slowly to eliminate the distortion.